The vanishing-viscosity error for quadratic Hamilton-Jacobi equations is of order ε log ε (not √ε), sharp in every dimension, with leading constant d/2.
The Cauchy problem for degenerate p arabolic equations
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Optimal rate of convergence in the vanishing viscosity for quadratic Hamilton-Jacobi equations
The vanishing-viscosity error for quadratic Hamilton-Jacobi equations is of order ε log ε (not √ε), sharp in every dimension, with leading constant d/2.